Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×A4×M32 |
| unambiguous semidirect product | (C23×M32)⋊C3 |
| Fitting, Sylow | C23×M32 ⋊ C3 |
539 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 539 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C22×A4×M32, A4×#2112, #72342027 |
| maximal normal subgroup of | C22×A4×M32, A4×#2112 |
| maximal quotient of | C22×A4×M32, A4×#2112 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084933);